You'll find a download link for the mod in the description of that YouTube video. Once you grab it (and have your legal backup of Super Mario 64 running in an emulator), just follow this tutorial video to host your own game or connect to a friend's. It is with great consternation that I must announce that, if you want to host a game, you will have to grapple with that fearsome beast called port forwarding; you can always ask for help on the official Super Mario 64 Online Discord server.

Also, for the sake of historical accuracy, I should note that Super Mario 64 has supported multiplayer players in the past; Super Mario 64 DS had a multiplayer mode waaaay back when it came out as a DS launch game in 2004. But that was limited to four players and only used specially designed arena stages. And, unbelievably, it didn't let you play as Waluigi. We were so deprived back then.

If you enjoy this kind of Super Mario 64 weirdness, consider signing up for modder Kaze Emanuar's Patreon. They're not far off from the "make this my actual job" goal and I can only imagine what kind of bizarre goodness could emerge from a full-time effort.